Name
12.1
?
Geometry and
Measurement—5.6.A
MATHEMATICAL PROCESSES
5.1.E, 5.1.F
Unit Cubes and Solid Figures
Essential Question
What is a unit cube and how can you use it to build
a solid figure?
Hands
On
Investigate
Investigate
You can build rectangular prisms using unit cubes. How many
different rectangular prisms can you build with a given number
of unit cubes?
Materials ■ centimeter cubes
A unit cube is a cube that has a length, width, and height
face
of 1 unit. A cube has _ square faces. All of its faces
are congruent. It has _ edges. The lengths of all its
edges are equal.
edge
1 unit
A. Build a rectangular prism with 2 unit cubes.
Think: When the 2 cubes are pushed together, the faces and edges
that are pushed together make 1 face and 1 edge.
• How many faces does the rectangular prism have? _
• How many edges does the rectangular prism have? _
B. Build as many different rectangular prisms as you can
with 8 unit cubes.
C. Record in units the dimensions of each rectangular prism
you built with 8 cubes.
Dimensions
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Math Talk
Mathematical Processes
Describe the different
rectangular prisms that you can
make with 4 unit cubes.
So, with 8 unit cubes, I can build _ different rectangular prisms.
Module 12
435
Make
Make Connections
Connections
You can build other solid figures and compare the solid figures
by counting the number of unit cubes.
3
4
5
6
1
2
1
2
3
4
5
Figure 1
Figure 2
Figure 1 is made up of _ unit cubes.
Figure 2 is made up of _ unit cubes.
So, Figure _ has more unit cubes than Figure _.
• Use 12 unit cubes to build a solid figure that is not a rectangular prism.
Share your model with a partner. Describe how your model is the same
and how it is different from your partner’s model.
Share
Share and
and Show
Show
Count the number of cubes used to build each solid figure.
1. The rectangular prism is made up of _ unit cubes.
_ unit cubes
5.
_ unit cubes
_ unit cubes
7.
6.
_ unit cubes
436
4.
3.
_ unit cubes
_ unit cubes
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2.
Name
Problem
Problem Solving
Solving
8.
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9.
How are the rectangular prisms in Exercises 3 and
4 related? Is there a different rectangular prism with the same
relationship? Use a model or a diagram to show your answer.
Write Math
Explain why a rectangular prism composed of
2 unit cubes has 6 faces. How do its dimensions compare to a unit cube?
Write Math
10.
Explain how the number of edges for the
rectangular prism compares to the number of edges for the unit cube.
11.
Multi-Step The Nakagin Capsule Tower
has 140 modules, and is 14 stories high. If all of the
modules were divided evenly among the number
of stories, how many modules would be on each floor?
How many different rectangular prisms could be made
from that number?
12.
A cube-shaped house can hold 1,000 unit cubes that are
1 meter by 1 meter by 1 meter. Describe the dimensions of the house
using unit cubes.
Module 12 • Lesson 1
437
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
13. Multi-Step Seth makes 3 more of the figure shown below to build a
fort. How many cubes does he use?
A
5 cubes
C
4 cubes
B
25 cubes
D
20 cubes
14. How many cubes were used to make the figure?
A
7 cubes
C
8 cubes
B
9 cubes
D
10 cubes
15. Multi-Step Alexandra built these two figures. How many cubes
did she use in all?
A
9 cubes
B
6 cubes
C
15 cubes
D
30 cubes
TEXAS Test Prep
16. Multi-Step How many more cubes can Marcy use to make the figure
438
A
5 cubes
C
2 cubes
B
13 cubes
D
7 cubes
© Houghton Mifflin Harcourt Publishing Company
below a rectangular prism?
Geometry and Measurement—5.6.A
MATHEMATICAL PROCESSES 5.1.E, 5.1.F
H o mewo rk
and Practice
12.1
Name
Unit Cubes and Solid Figures
Count the number of cubes used to build each solid figure.
1.
2.
_ unit cubes
4.
3.
_ unit cubes
5.
_ unit cubes
7.
6.
_ unit cubes
8.
_ unit cubes
_ unit cubes
_ unit cubes
9.
_ unit cubes
_ unit cubes
© Houghton Mifflin Harcourt Publishing Company
Problem
Problem Solving
Solving
10. Jen used unit cubes to build a rectangular prism
11. Mrs. Hernandez keeps her classroom supply of
with a length of 4 cubes, a width of 3 cubes,
and height of 5 cubes. Ethan built a rectangular
prism with a length of 3 cubes, a width of
3 cubes and a height of 6 cubes. Who used more
cubes? Explain.
centimeter cubes in a box that is 20 cm by 6 cm
by 3 cm. How many centimeter cubes will fill
the box?
Module 12 • Lesson 1
439
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
unit cubes. How many cubes does Blaine use?
A
14 cubes
C
10 cubes
B
20 cubes
D
9 cubes
14. Lola has 30 cubes. She wants to use all the
cubes to make a rectangular prism. Which
could be the dimensions of her prism?
A
5×2×3
B
3×3×3
C
4×5×2
D
3 × 10 × 2
16. Multi-Step Stella built these two figures. How
many more cubes did she use in figure A than
in figure B?
A
440
B
A
8 cubes
C
3 cubes
B
5 cubes
D
2 cubes
13. Lucas covers a rectangle with 5 rows of 4 unit
cubes. Then he stacks identical layers to make
a prism. How many cubes does Lucas use to
make 4 layers?
A
80 cubes
B
20 cubes
C
100 cubes
D
24 cubes
15. Multi-Step How many cubes will be in the
figure shown below if 12 cubes are added?
A
36 cubes
C
48 cubes
B
24 cubes
D
60 cubes
17. Multi-Step Owen wants to make a
rectangular prism with a length of 6 cubes, a
width of 3 cubes, and a height of 4 cubes. He
has 54 cubes. How many more cubes does
Owen need?
A
36 cubes
B
42 cubes
C
22 cubes
D
18 cubes
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12. Blaine makes the figure shown below using